Micro-packets for real groups of type $G_2$

TL;DR

This paper computes all micro-packets for real groups of type G_2 by analyzing Weyl group actions on characteristic cycles, advancing understanding of Arthur's conjectures through microlocal geometric methods.

Contribution

It introduces a method to explicitly determine micro-packets for G_2, utilizing Weyl group actions on characteristic cycles, which was not previously done.

Findings

All micro-packets for real G_2 groups are explicitly computed.

Weyl group actions on characteristic cycles are effectively used for this computation.

The results support the microlocal geometric approach to Arthur's conjectures.

Abstract

In their study of Arthur's conjectures for real groups, Adams, Barbasch, and Vogan introduced the notion of micro-packets. Micro-packets are finite sets of irreducible representations defined using microlocal geometric methods and characteristic cycles. We explore an action of the Weyl group on characteristic cycles to compute all micro-packets of real groups of type $G_2$.